Modern cars have a rather complicated design. However, the principle of operation of their systems is based on the use of simple mechanisms. One of them is leverage. What is it from the point of view of physics, and also, under what condition is the lever in equilibrium? We will answer these and other questions in the article.
Leverage in Physics
Everyone is well aware of what kind of mechanism this is. In physics, a lever is a structure consisting of two parts - a beam and a support. A beam can be a board, a rod, and any other solid object having a certain length. The support, located below the beam, is the equilibrium point of the mechanism. It ensures that the lever has an axis of rotation, divides it into two shoulders and prevents the translational movement of the system in space.
Since ancient times, humanity has been using the lever mainly to facilitate the work of lifting heavy loads. However, this mechanism has wider application. So it can be used to give the cargo a big boost. A striking example of this application are medieval catapults.
Leverage acting
To make it easier to consider the forces that have an effect on the shoulders of the lever, consider the following figure:
We see that this mechanism has shoulders of different lengths (d R <d F ). Two forces act on the edges of the shoulders, which are directed downward. External force F tends to lift the load R and do useful work. The load R resists this rise.
In fact, there is a third force acting in this system - the reaction of support. However, it does not interfere and does not contribute to the rotation of the lever around the axis, it only ensures the absence of translational movement of the entire system.
Thus, the balance of the lever is determined by the ratio of only two forces: F and R.
The equilibrium condition of the mechanism
Before writing down the formula for the equilibrium of the lever, we consider one important physical characteristic of the rotational motion - the moment of force. By it we mean the product of the shoulder d by the force F:
M = d * F.
This formula is valid when the force F acts perpendicular to the lever arm. The quantity d describes the distance from the fulcrum (axis of rotation) to the point of application of force F.
Remembering the statics, we note that the system will not rotate around its axes if the sum of all its moments is zero. When finding this amount should also take into account the sign of the moment of force. If the force in question tends to make a counterclockwise rotation, then the moment it creates will be positive. Otherwise, when calculating the moment of force, you should take it with a negative sign.
Applying the above condition of rotational equilibrium for the lever, we obtain the following equality:
d R * R - d F * F = 0.
Transforming this equality, we can write this:
d R / d F = F / R.
The last expression is the leverage balance formula. Equality suggests that: the greater the leverage d F compared to d R , the less force F will need to be applied to balance the load R.
The formula for the leverage balance given using the concept of the moment of force was first experimentally obtained by Archimedes in the 3rd century BC. e. But he received it exclusively by experiment, since at that time the concept of the moment of force was not introduced into physics.
The written condition for the equilibrium of the lever also allows us to understand why this simple mechanism makes it possible to win either in the way or in strength. The fact is that when you turn the shoulders of the lever, a greater distance passes a longer one. At the same time, it is affected by a smaller force than the short one. In this case, we get a gain in strength. If the shoulder parameters are left the same, and the load and force are interchanged, then we get a gain on the way.
The task of determining equilibrium
The length of the lever beam is 2 meters. The support is located at a distance of 0.5 meters from the left end of the beam. It is known that the lever is in equilibrium and a force of 150 N acts on its left shoulder. What mass should be put on the right shoulder so that it balances this force.
To solve this problem, we apply the equilibrium rule, which was written above, we have:
d R / d F = F / R =>
1.5 / 0.5 = 150 / R =>
R = 50 N.
Thus, the weight of the cargo should be equal to 50 N (not to be confused with the mass). We translate this value into the corresponding mass using the formula for gravity, we have:
m = R / g = 50 / 9.81 = 5.1 kg.
A body weighing only 5.1 kg will balance a force of 150 N (this value corresponds to a body weight of 15.3 kg). This indicates a threefold gain in strength.